Theorems · Theorem · commutative algebra
descPochhammer_succ_eval
∀ {S : Type u_1} [inst : Ring S] (n : ℕ) (k : S),
Polynomial.eval k (descPochhammer S (n + 1)) = Polynomial.eval k (descPochhammer S n) * (k - ↑n)- Defined in
- Mathlib.RingTheory.Polynomial.Pochhammer
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- Polynomialproof · cited by 5,681
- Polynomial.Xproof · cited by 1,639
- Polynomial.evalstatement and proof · cited by 796
- mul_subproof · cited by 201
- Polynomial.eval_subproof · cited by 124
- descPochhammerstatement and proof · cited by 51
- Polynomial.C_eq_natCastproof · cited by 25
- Nat.cast_commproof · cited by 16
- descPochhammer_succ_rightproof · cited by 14
- Polynomial.eval_mul_Xproof · cited by 11
- Polynomial.eval_C_mulproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- descPochhammer_eval_eq_ascPochhammerproof · cited by 4
- monotoneOn_descPochhammer_evalproof · cited by 0
- pow_le_descPochhammer_evalproof · cited by 0